reserve G,G1,G2 for _Graph;
reserve e,x,y for set;
reserve v,v1,v2 for Vertex of G;
reserve W for Walk of G;

theorem
  for G1 being _Graph, G2 being Subgraph of G1, v1 being Vertex of G1,
v2 being Vertex of G2 st v1 = v2 holds G2.reachableFrom(v2) c= G1.reachableFrom
  (v1)
proof
  let G1 be _Graph, G2 be Subgraph of G1, v1 be Vertex of G1, v2 be Vertex of
  G2;
  assume
A1: v1 = v2;
  let v be object;
  assume v in G2.reachableFrom(v2);
  then consider W being Walk of G2 such that
A2: W is_Walk_from v2,v by Def5;
  reconsider W2=W as Walk of G1 by GLIB_001:167;
  W2 is_Walk_from v1,v by A1,A2,GLIB_001:19;
  hence thesis by Def5;
end;
